Paving system

ABSTRACT

A paving system is disclosed that includes a first paving stone having a virtual perimeter outline and a plurality of first physical sides, the virtual perimeter outline having a plurality of segments, where each segment of the plurality of segments corresponds to two or more of the first physical sides, and wherein any vertex between two adjacent segments is separated from any vertex between two adjacent first physical sides by a predetermined distance. A second paving stone having the virtual perimeter outline and a plurality of second physical sides, where each segment of the plurality of segments corresponds to two or more of the second physical sides, and wherein any vertex between two adjacent segments is separated from any vertex between two adjacent second physical sides by a predetermined distance. The plurality of first physical sides is different from the plurality of second physical sides.

RELATED APPLICATIONS

The present application is a continuation-in-part of pending U.S. Designpatent application No. 29/543,176, filed Oct. 21, 2015.

TECHNICAL FIELD

The present disclosure relates generally to a paving system, and morespecifically to a paving system that utilizes a Cairo pentagon as aguide for a set of different paver shapes.

BACKGROUND OF THE INVENTION

Paving systems are known that use different pavers, but despite the useof different pavers, an irregular appearance that avoids repeatingconfigurations is not known.

SUMMARY OF THE INVENTION

A paving system is disclosed that includes a first paving stone having avirtual perimeter outline and a plurality of first physical sides, wherethe virtual perimeter outline has a plurality of segments, where eachsegment of the plurality of segments corresponds to two or more of thefirst physical sides, and wherein any vertex between two adjacentsegments is separated from any vertex between two adjacent firstphysical sides by a predetermined distance. A second paving stone hasthe virtual perimeter outline and a plurality of second physical sides,where each segment of the plurality of segments corresponds to two ormore of the second physical sides, and wherein any vertex between twoadjacent segments is separated from any vertex between two adjacentsecond physical sides by a predetermined distance. The plurality offirst physical sides is different from the plurality of second physicalsides.

Other systems, methods, features, and advantages of the presentdisclosure will be or become apparent to one with skill in the art uponexamination of the following drawings and detailed description. It isintended that all such additional systems, methods, features, andadvantages be included within this description, be within the scope ofthe present disclosure, and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Aspects of the disclosure can be better understood with reference to thefollowing drawings. The components in the drawings may be to scale, butemphasis is placed upon clearly illustrating the principles of thepresent disclosure. Moreover, in the drawings, like reference numeralsdesignate corresponding parts throughout the several views, and inwhich:

FIG. 1 is an isometric projection of a first paving stone in accordancewith an exemplary embodiment of the present disclosure;

FIG. 2 is a top view of a first paving stone in accordance with anexemplary embodiment of the present disclosure;

FIG. 3 is an isometric projection of a second paving stone in accordancewith an exemplary embodiment of the present disclosure;

FIG. 4 is a top view of a second paving stone in accordance with anexemplary embodiment of the present disclosure;

FIG. 5 is an isometric projection of a third paving stone in accordancewith an exemplary embodiment of the present disclosure;

FIG. 6 is a top view of a third paving stone in accordance with anexemplary embodiment of the present disclosure;

FIG. 7 is an isometric projection of a fourth paving stone in accordancewith an exemplary embodiment of the present disclosure;

FIG. 8 is a top view of a fourth paving stone in accordance with anexemplary embodiment of the present disclosure;

FIG. 9 is an isometric projection of a fifth paving stone in accordancewith an exemplary embodiment of the present disclosure;

FIG. 10 is a top view of a fifth paving stone in accordance with anexemplary embodiment of the present disclosure; and

FIG. 11 is a layout diagram showing a plurality of first paving stones,second paving stones, third paving stones, fourth paving stones andfifth paving stones arranged in a Cairo pentagon pattern, in accordancewith an exemplary embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE INVENTION

In the description that follows, like parts are marked throughout thespecification and drawings with the same reference numerals. The drawingfigures may be to scale and certain components can be shown ingeneralized or schematic form and identified by commercial designationsin the interest of clarity and conciseness.

Prior art paving systems includes those where the pavers are differentlysized units, each of which is an integer multiple of a basic rotationaltessellation element. This configuration has the effect of interruptingthe joint pattern and making the pavers less regular in appearance.Although the various units fit together, it is difficult for aninstaller to assemble the pavers, and this idea has largely failed inthe marketplace.

Another prior art paving system is the single-piece system, wherein allof the units are of the same size and form a repeating pattern that iseasier to install. The repeating pattern is disguised in part by falsejoints in the stones themselves, but the single piece system, whichunavoidably has a joint surrounding each unit, also has limitations thatrender it unacceptable. First, the sides of the stones generally extendfrom the vertices of the tessellation. So, although the joints areirregularly shaped, they intersect at regular intervals along a straightline, and the joints meet in perfect crossing alignment with each other.These characteristics degrade the illusion of randomness in thecompleted pavement.

Second, sides of adjacent stones have the same length, which introducesanother degree of artificiality, and which further degrades the illusionof randomness. Third, the sides of adjacent stones are rotational imagesof one another, and have the same configuration with only minorvariations in the sides. This characteristic limits the ability toimitate hand-split flagstone, which rarely fractures into polygons ofany significant concavity. The result is sides which conform closely,and revealingly, to those of the base tessellation array, because forone stone to depart from the array in a credible, convex way requiresthe adjacent stone to have an incredible, concave side.

Fourth, the use of 120 degree rotational tessellations makes layout andinstallation difficult for workmen accustomed to rectilineararrangements. Constructing a rectangular pavement requires either 1)overlaying and trimming the perimeter, which is costly, or 2) employinga variety of specially-configured termination blocks, which createsestimating and inventory challenges.

The present disclosure addresses these problems. In one exemplaryembodiment, pavers derived from a Cairo pentagonal tiling are used toform the arrangement of stones. The arrangement is fundamentallyorthogonal, integrates more readily with common landscape features (suchas rectangular building foundations), and is simple to lay-out withcommon tools such as try squares, string lines, and Pythagoreantriangles.

Second, although the perimeter of each stone fits within a commonblock-bounding polygon, the vertices of the polygon are substantiallydisplaced from the vertices of its associated Cairo pentagon, resultingin joints that intersect imperfectly with each other, and also in themisalignment of the joint intersections with the axes of the tilingarray.

Third, the misalignment of the joint intersections results in abuttingsides of adjacent stones having different lengths, which also helps toobscure the Cairo-pentagonal shape that is the basis of each paver.Fourth, the sides of adjacent stones are not images of one another.Instead, substantial gaps, notches, and intersecting false joints on oneside of a joint bear no complementary resemblance to the side of thestone on the opposite side of the joint.

Fifth, the disclosed block-bounding polygon is significantly concave,and the stones inscribed therein include false joints to visuallysubdivide them into multiple substantially convex polygons, whichconform to the usual appearance of flagstone. Sixth, the Cairo pentagonis easily subdivided into two termination stones, which together innormal arrangement can replace a whole stone in the array, together inabutting arrangement can form a straight edge termination, and pairsthereof can easily form outside 90 degree corners.

One aspect of the present disclosure is the avoidance of rotationalimages, which improves the ability to avoid readily observable repeatingpatterns. Rotational images are avoided by using perimeter segments thatdo not mate or conform to each other, but which also do not interferewith each other. In addition, multiple sides are used to form theperimeter segments for adjacent pavers, which improves the ability toavoid rotational images, mating sides and other inferior features thatresult in readily discernable repeating patterns.

FIG. 1 is an isometric projection of a first paving stone 100, inaccordance with an exemplary embodiment of the present disclosure.Paving stone 100 and all other paving stones disclosed herein can beformed from concrete, masonry or other suitable materials, can be wetcast, dry cast or manufactured in other suitable manners.

As used herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof. As used herein, the term “and/or”includes any and all combinations of one or more of the associatedlisted items. As used herein, phrases such as “between X and Y” and“between about X and Y” should be interpreted to include X and Y. Asused herein, phrases such as “between about X and Y” mean “between aboutX and about Y.” As used herein, phrases such as “from about X to Y” mean“from about X to about Y.”

Paving stone 100 includes false joints 102 and 104, which separate theupper surface of paving stone 100 into a large area 106, an intermediatearea 108 and a small area 110. In this manner, paving stone 100 appearsto be three different stones to a casual observer, and the false joints102 and 104 also help to channel water to the joints between pavingstone 100 and adjacent paving stones. Paving stone 100 also includesupper perimeter segment surface 112 and lower perimeter segment surface114, where upper perimeter segment surface 112 gradually decreases indiameter from the diameter of lower perimeter segment surface 114. Inthis manner, the minimum spacing between paving stone 100 and adjacentpaving stones can appear to be approximately the same as the spacing ofthe false joints.

FIG. 2 is a top view of a first paving stone 200, in accordance with anexemplary embodiment of the present disclosure. Cairo pentagon overlay202 shows the outline of an ideal or virtual Cairo pentagon, and theoutline of paving stone 200 can be seen to deviate from Cairo pentagonoverlay 202. In particular, a portion 210 of large section 204 extendssignificantly beyond the boundary of Cairo pentagon overlay 202, and thepoint of contact between large section 204 and small section 208 forms acorner of space 212 within Cairo pentagon overlay 202, where space 212is approximately equal in size to portion 210 of large section 204.Likewise, intermediate section 206 extends for a smaller section 214outside of Cairo pentagon overlay 202, and intermediate section 206forms a corner of space 216 with large section 204, where space 216 isapproximately the size of smaller section 214.

The perimeter of paving stone 200 is formed in one of twoconfigurations—either offset perimeter segment 218 or flat perimetersegment 220. Offset perimeter segment 218 is located along a continuoussection opposite from flat perimeter segment 220, and is oriented sothat paving stone 200 can be readily fitted with other paving stones ofthe disclosed paving system, by assembling the paving stones so that anoffset perimeter segment 218 is adjacent to a flat perimeter segment220, or in other suitable manners.

Each of the five perimeter segments 274, 276, 278, 280 and 282 areformed from multiple sides or portions of sides, so as to avoidrotational images. For example, perimeter segment 274 is formed from aportion of side 270, side 272 and a portion of side 250, and thus avoidsthe creation of a vertex where perimeter segment 274 meets withperimeter segment 276 or perimeter segment 282. Likewise, perimetersegment 276 is formed from a portion of side 250, side 252, side 254 anda portion of side 256, which avoids the creation of a vertex at theintersection of perimeter segment 276 and perimeter segment 278.Perimeter segment 278 is formed from a portion of side 256, side 258,side 260 and most of side 262, although it will be recognized by one ofskill in the art that the “sides” that are discussed herein with respectto every exemplary embodiment are not really sides, as they are formedfrom irregular shapes that are not straight line segments and are notamenable to characterization as a true “side.” Perimeter segment 280 isformed from a portion of side 262 and most of side 264, and perimetersegment 282 is formed from a portion of side 264, sides 266 and 268, andmost of side 270. As can be seen, no vertices are formed in paving stone200 that correspond to the intersection of perimeter segment 280 withperimeter segment 278 or perimeter segment 282.

Paving stone 200 also includes notches 222, 224 and 226, which are usedto improve the random appearance of paving stone 200 when it is used inconjunction with other pavers, and which also provides a space for waterto drain from the surface of paving stone 200.

Paving stone 200 thus has a bottom surface with a fixed orientationrelative to its associated Cairo pentagon. The perimeter of the bottomsurface encloses an area greater than about 90% of the area of the Cairopentagon, but can include greater or lesser areas as suitable. At leastabout 8% of the bottom surface falls outside the boundaries of the Cairopentagon, although more or less can fall outside as suitable. Inaddition, paving stone 200 has no vertices that coincide with thevertices of its associated Cairo pentagon, which helps to avoid thecreation of a rotational image. In application, the distance between aperimeter segment of paving stone 200 and a vertex of its associatedCairo pentagon can be within about 10 mm or other suitable distances,can be within about 5% of the total length of the perimeter or othersuitable distances, and can have other suitable unique or repeatingfeatures. Likewise, while a Cairo pentagon is used in the disclosedembodiments, other suitable shapes can be used as the basis for a pavingstone in accordance with the present disclosure, where the paving stonehas the other disclosed features and functional attributes as disclosedherein.

While it is recognized that paving stone 200 and other paving stones asdisclosed herein also have certain non-functional and ornamentalattributes, the ability to have a paving stone system with a smallnumber of different stones that nonetheless creates a random appearanceprovides the functional attributes of reducing an amount of manual workthat is required to create a paving stone layout with a randomappearance, reducing the number of different types of paving stones thatneed to be kept on site to create a random appearing paving stonesection, facilitating the easy placement of paving stones within acommon rectangular space while maintaining a random appearance, andnumerous other benefits as further discussed and disclosed herein, suchas facilitating the drainage of water from the surface of the pavingstones.

FIG. 3 is an isometric projection of a second paving stone 300, inaccordance with an exemplary embodiment of the present disclosure.Paving stone 300 includes false joints 302 and 304, which separate theupper surface of paving stone 300 into a large area 306, an intermediatearea 308 and a small area 310. In this manner, paving stone 300 appearsto be three different stones to a casual observer, and the false joints302 and 304 also help to channel water to the joints between pavingstone 300 and adjacent paving stones. Paving stone 300 also includesupper perimeter segment surface 312 and lower perimeter segment surface314, where upper perimeter segment surface 312 gradually decreases indiameter from the diameter of lower perimeter segment surface 314. Inthis manner, the minimum spacing between paving stone 300 and adjacentpaving stones can appear to be approximately the same as the spacing ofthe false joints.

FIG. 4 is a top view of a second paving stone 400, in accordance with anexemplary embodiment of the present disclosure. Cairo pentagon overlay402 shows the outline of an ideal Cairo pentagon, and the outline ofpaving stone 400 can be seen to deviate from Cairo pentagon overlay 402.In particular, a portion 410 of large section 404 extends significantlybeyond the boundary of Cairo pentagon overlay 402, and the point ofcontact between large section 404 and intermediate section 406 forms acorner of space 412 within Cairo pentagon overlay 402, where space 412that is approximately equal in size to portion 410 of large section 404.Likewise, large section 404 extends for a smaller section 414 outside ofCairo pentagon overlay 402, and small section 408 forms a corner ofspace 416 with large section 404, where space 416 is approximately thesize of smaller section 414.

The perimeter of paving stone 400 is formed in one of twoconfigurations—either offset perimeter segment 418 or flat perimetersegment 420. Offset perimeter segment 418 is located along a continuoussection opposite from flat perimeter segment 420, and is oriented sothat paving stone 400 can be readily fitted with other paving stones ofthe disclosed paving system, by assembling the paving stones so thatoffset perimeter segment 418 is adjacent to flat perimeter segments 420,or in other suitable manners.

Perimeter segment 428 is formed from a portion of side 468, side 438 anda portion of side 440. Perimeter segment 430 is formed from a portion ofside 440, sides 442, 444, 446 and 448 and a portion of side 450.Perimeter segment 432 is formed from a portion of side 450, sides 452,454 and 456 and most of side 458. Perimeter segment 434 is formed from aportion of side 458 and most of side 460. Perimeter segment 436 isformed from a portion of side 460, sides 462, 464 and 466, and most ofside 468. The vertices of perimeter segments 428, 430, 432, 434 and 436do not coincide with any vertex of sides of paving stone 400, and thusavoid any rotational images. In addition, the large number of sides ofpaving stone 400 and the variations in the number of sides of perimetersegments 428, 430, 432, 434 and 436 results in non-matching perimetersegments that are not rotational images of other perimeter segments, andwhich do not match perimeter segments on other paving stones, whichhelps to avoid the creation of easily-observable repeating patternswhile simplifying installation.

Paving stone 400 also includes notches 422, 424 and 426, which are usedto improve the random appearance of paving stone 400 when it is used inconjunction with other pavers, and which also provides a space for waterto drain from the surface of paving stone 400.

Paving stone 400 thus has a bottom surface with a fixed orientationrelative to its associated Cairo pentagon. The perimeter of the bottomsurface encloses an area greater than about 90% of the area of the Cairopentagon, but can include greater or lesser areas as suitable. At leastabout 8% of the bottom surface falls outside the boundaries of the Cairopentagon, although more or less can fall outside as suitable. Inaddition, paving stone 400 has no vertices that coincide with a vertexof its associated Cairo pentagon, which also helps to avoid the creationof a rotational image. In application, the distance between a perimetersegment of paving stone 400 and a vertex of its associated Cairopentagon can be within about 10 mm or other suitable distances, can bewithin about 5% of the total length of the perimeter or other suitabledistances, and can have other suitable unique or repeating features.Likewise, while a Cairo pentagon is used in the disclosed embodiments,other suitable shapes can be used as the basis for a paving stone inaccordance with the present disclosure, where the paving stone has theother disclosed features and functional attributes as disclosed herein.

FIG. 5 is an isometric projection of a third paving stone 500, inaccordance with an exemplary embodiment of the present disclosure.Paving stone 500 includes false joints 502 and 504, which separate theupper surface of paving stone 500 into a large area 506, an intermediatearea 508 and a small area 510. In this manner, paving stone 500 appearsto be three different stones to a casual observer, and the false joints502 and 504 also help to channel water to the joints between pavingstone 500 and adjacent paving stones. Paving stone 500 also includesupper perimeter segment surface 512 and lower perimeter segment surface514, where upper perimeter segment surface 512 gradually decreases indiameter from the diameter of lower perimeter segments surface 514. Inthis manner, the minimum spacing between paving stone 500 and adjacentpaving stones can appear to be approximately the same as the spacing ofthe false joints.

FIG. 6 is a top view of a third paving stone 600, in accordance with anexemplary embodiment of the present disclosure. Cairo pentagon overlay602 shows the outline of an ideal Cairo pentagon, and the outline ofpaving stone 600 can be seen to deviate from Cairo pentagon overlay 602.In particular, a portion 610 of intermediate section 606 extendssignificantly beyond the boundary of Cairo pentagon overlay 602, and thepoint of contact between large section 604 and intermediate section 606forms a corner of space 612 within Cairo pentagon overlay 602, wherespace 612 is approximately equal in size to portion 610 of intermediatesection 606. Likewise, small section 608 extends for a smaller section614 outside of Cairo pentagon overlay 602, and small section 608 forms acorner of space 616 with large section 604, where space 616 isapproximately the size of smaller section 614.

The perimeter of paving stone 600 is formed in one of twoconfigurations—either offset perimeter segment 618 or flat perimetersegment 620. Offset perimeter segment 618 is located along a continuoussection opposite from flat perimeter segment 620, and is oriented sothat paving stone 600 can be readily fitted with other paving stones ofthe disclosed paving system, by assembling the paving stones so thatoffset perimeter segment 618 is adjacent to flat perimeter segment 620,or in other suitable manners.

Perimeter segment 628 is formed from a portion of side 668, side 670 anda portion of side 638. Perimeter segment 630 is formed from a portion ofside 638, sides 640 and 642, and a portion of side 644. Perimetersegment 632 is formed from a portion of side 644, side 646 and a portionof side 648. Perimeter segment 634 is formed from a portion of side 648,sides 650, 652, 654, 656, 658, 660 and a portion of side 662. Perimetersegment 636 is formed from a portion of side 662, sides 664 and 666, anda portion of side 668. The vertices of perimeter segments 628, 630, 632,634 and 636 do not coincide with any vertex of sides of paving stone600, and thus avoid any rotational images. In addition, the large numberof sides of paving stone 600 and the variations in the number of sidesof perimeter segments 628, 630, 632, 634 and 636 results in non-matchingperimeter segments that are not rotational images of other perimetersegments, and which do not match perimeter segments on other pavingstones, which helps to avoid the creation of easily-observable repeatingpatterns while simplifying installation.

Paving stone 600 also includes notches 622, 624 and 626, which are usedto improve the random appearance of paving stone 600 when it is used inconjunction with other pavers, and which also provides a space for waterto drain from the surface of paving stone 600.

Paving stone 600 thus has a bottom surface with a fixed orientationrelative to its associated Cairo pentagon. The perimeter of the bottomsurface encloses an area greater than about 90% of the area of the Cairopentagon, but can include greater or lesser areas as suitable. At leastabout 8% of the bottom surface falls outside the boundaries of the Cairopentagon, although more or less can fall outside as suitable. Inaddition, paving stone 600 has no vertices that coincide with a vertexof its associated Cairo pentagon. In application, the distance between aperimeter segment of paving stone 600 and a vertex of its associatedCairo pentagon can be within about 10 mm or other suitable distances,can be within about 5% of the total length of the perimeter or othersuitable distances, and can have other suitable unique or repeatingfeatures. Likewise, while a Cairo pentagon is used in the disclosedembodiments, other suitable shapes can be used as the basis for a pavingstone in accordance with the present disclosure, where the paving stonehas the other disclosed features and functional attributes as disclosedherein.

FIG. 7 is an isometric projection of a fourth paving stone 700, inaccordance with an exemplary embodiment of the present disclosure.Paving stone 700 includes false joint 702, which separates the uppersurface of paving stone 700 into a large area 704 and a small area 706.In this manner, paving stone 700 appears to be three different stones toa casual observer, and the false joint 702 also helps to channel waterto the joints between paving stone 700 and adjacent paving stones.Paving stone 700 also includes upper perimeter segment surface 708 andlower perimeter segment surface 710, where upper perimeter segmentsurface 708 gradually decreases in diameter from the diameter of lowerperimeter segment surface 710. In this manner, the minimum spacingbetween paving stone 700 and adjacent paving stones can appear to beapproximately the same as the spacing of the false joints.

FIG. 8 is a top view of a fourth paving stone 800, in accordance with anexemplary embodiment of the present disclosure. Cairo pentagon overlay802 shows the outline of an ideal Cairo pentagon, and the outline ofpaving stone 800 can be seen to deviate from Cairo pentagon overlay 802.In particular, a portion 808 of large section 804 extends significantlybeyond the boundary of Cairo pentagon overlay 802, and the point ofcontact between large section 804 and small section 806 forms a cornerof space 810 within Cairo pentagon overlay 802, where space 810 isapproximately equal in size to portion 808 of large section 804.Likewise, small section 806 extends for a smaller section 812 outside ofCairo pentagon overlay 802, and small section 806 forms a corner ofspace 814 with large section 804, where space 814 is approximately thesize of smaller section 812.

The perimeter of paving stone 800 is formed in one of twoconfigurations—either offset perimeter segment 816 or flat perimetersegment 818. Offset perimeter segment 816 is located along a continuoussection opposite from flat perimeter segment 818, and is oriented sothat paving stone 800 can be readily fitted with other paving stones ofthe disclosed paving system, by assembling the paving stones so thatoffset perimeter segment 816 is adjacent to flat perimeter segment 818,or in other suitable manners.

Perimeter segment 824 is formed from a portion of side 848, side 832 anda portion of side 834. Perimeter segment 826 is formed from a portion ofside 834, sides 836 and 838, and a portion of side 840. Perimetersegment 828 is formed from a portion of side 840, sides 842 and 844, anda portion of side 846. Perimeter segment 830 is formed from a portion ofside 846 and a portion of side 848. The vertices of perimeter segments824, 826, 828, 830 and 832 do not coincide with any vertex of sides ofpaving stone 800, and thus avoid any rotational images. In addition, thelarge number of sides of paving stone 800 and the variations in thenumber of sides of perimeter segments 824, 826, 828, 830 and 832 resultsin non-matching perimeter segments that are not rotational images ofother perimeter segments, and which do not match perimeter segments onother paving stones, which helps to avoid the creation ofeasily-observable repeating patterns while simplifying installation.

Paving stone 800 also includes notches 820 and 822, which are used toimprove the random appearance of paving stone 800 when it is used inconjunction with other pavers, and which also provides a space for waterto drain from the surface of paving stone 800.

Paving stone 800 thus has a bottom surface with a fixed orientationrelative to its associated Cairo pentagon. The perimeter of the bottomsurface encloses an area greater than about 90% of the area of the Cairopentagon, but can include greater or lesser areas as suitable. At leastabout 8% of the bottom surface falls outside the boundaries of the Cairopentagon, although more or less can fall outside as suitable. Inaddition, paving stone 800 has no vertices that coincide with a vertexof its associated Cairo pentagon. In application, the distance between aperimeter segment of paving stone 800 and a vertex of its associatedCairo pentagon can be within about 10 mm or other suitable distances,can be within about 5% of the total length of the perimeter or othersuitable distances, and can have other suitable unique or repeatingfeatures. Likewise, while a Cairo pentagon is used in the disclosedembodiments, other suitable shapes can be used as the basis for a pavingstone in accordance with the present disclosure, where the paving stonehas the other disclosed features and functional attributes as disclosedherein.

FIG. 9 is an isometric projection of a fifth paving stone 900, inaccordance with an exemplary embodiment of the present disclosure.Paving stone 900 includes false joints 902, 904 and 906, which separatethe upper surface of paving stone 300 into three areas 908, 910 and 912of approximately equal size. In this manner, paving stone 900 appears tobe three different stones to a casual observer, and the false joints902, 904 and 906 also help to channel water to the joints between pavingstone 900 and adjacent paving stones. Paving stone 900 also includesupper perimeter segment surface 914 and lower perimeter segment surface916, where upper perimeter segment surface 914 gradually decreases indiameter from the diameter of lower perimeter segment surface 916. Inthis manner, the minimum spacing between paving stone 900 and adjacentpaving stones can appear to be approximately the same as the spacing ofthe false joints.

FIG. 10 is a top view of a fifth paving stone 1000, in accordance withan exemplary embodiment of the present disclosure. Cairo pentagonoverlay 1002 shows the outline of an ideal Cairo pentagon, and theoutline of paving stone 1000 can be seen to deviate from Cairo pentagonoverlay 1002. In particular, a portion 1010 of section 1008 extendssignificantly beyond the boundary of Cairo pentagon overlay 1002, andthe point of contact between section 1008 and section 1006 forms acorner of space 1012 within Cairo pentagon overlay 1002, where space1012 is approximately equal in size to portion 1010 of section 1008.Likewise, section 1006 extends for a smaller section 1014 outside ofCairo pentagon overlay 1002, and section 1004 forms a corner of space1016 with section 1006, where space 1016 is approximately the size ofsmaller section 1014.

The perimeter of paving stone 1000 is formed in one of twoconfigurations—either offset perimeter segment 1018 or flat perimetersegment 1020. Offset perimeter segment 1018 is located along acontinuous section opposite from flat perimeter segment 1020, and isoriented so that paving stone 1000 can be readily fitted with otherpaving stones of the disclosed paving system, by assembling the pavingstones so that offset perimeter segment 1018 is adjacent to flatperimeter segment 1020, or in other suitable manners.

Perimeter segment 1028 is formed from a portion of sides 1064 and 1036.Perimeter segment 1030 is formed from a portion of side 1036, sides1038, 1040, 1042, 1044 and a portion of 1046. Perimeter segment 1032 isformed from a portion of side 1046, sides 1048, 1050, 1052, 1054 and aportion of side 1056. Perimeter segment 1034 is formed from a portion ofside 1056, sides 1058, 1060, 1062 and a portion of side 1064. Thevertices of perimeter segments 1028, 1030, 1032 and 1034 do not coincidewith any vertex of sides of paving stone 1000, and thus avoid anyrotational images. In addition, the large number of sides of pavingstone 1000 and the variations in the number of sides of perimetersegments 1028, 1030, 1032 and 1034 results in non-matching perimetersegments that are not rotational images of other perimeter segments, andwhich do not match perimeter segments on other paving stones, whichhelps to avoid the creation of easily-observable repeating patternswhile simplifying installation.

Paving stone 1000 also includes notches 1022, 1024 and 1026, which areused to improve the random appearance of paving stone 1000 when it isused in conjunction with other pavers, and which also provides a spacefor water to drain from the surface of paving stone 1000.

Paving stone 1000 thus has a bottom surface with a fixed orientationrelative to its associated Cairo pentagon. The perimeter of the bottomsurface encloses an area greater than about 90% of the area of the Cairopentagon, but can include greater or lesser areas as suitable. At leastabout 8% of the bottom surface falls outside the boundaries of the Cairopentagon, although more or less can fall outside as suitable. Inaddition, paving stone 1000 has no vertices that coincide with a vertexof its associated Cairo pentagon. In application, the distance between aperimeter segment of paving stone 1000 and a vertex of its associatedCairo pentagon can be within about 10 mm or other suitable distances,can be within about 5% of the total length of the perimeter or othersuitable distances, and can have other suitable unique or repeatingfeatures. Likewise, while a Cairo pentagon is used in the disclosedembodiments, other suitable shapes can be used as the basis for a pavingstone in accordance with the present disclosure, where the paving stonehas the other disclosed features and functional attributes as disclosedherein.

FIG. 11 is a diagram 1100 showing a plurality of first paving stones1102, second paving stones 1104, third paving stones 1106, fourth pavingstones 1108 and fifth paving stones 1110 arranged in a Cairo pentagonpattern, in accordance with an exemplary embodiment of the presentdisclosure. Diagram 1100 shows an exemplary arrangement of first pavingstones 1102, second paving stones 1104, third paving stones 1106, fourthpaving stones 1108 and fifth paving stones 1110 that results in arectangular shape, and which demonstrates the manner in which themodified Cairo pentagons of the present disclosure can be easilyarranged in patterns that are difficult to discern but which can beimplemented using only five different pavers. As can be readily seen,there are no matching sides, and no side is a rotational image ofanother side.

It should be emphasized that the above-described embodiments are merelyexamples of possible implementations. Many variations and modificationsmay be made to the above-described embodiments without departing fromthe principles of the present disclosure. All such modifications andvariations are intended to be included herein within the scope of thisdisclosure and protected by the following claims.

What is claimed is:
 1. A paving system comprising: a first paving stonehaving a virtual perimeter outline and a plurality of first physicalsides, the virtual perimeter outline having a plurality of segments,where each segment of the plurality of segments corresponds to two ormore of the first physical sides, and wherein any vertex between twoadjacent segments is separated from any vertex between two adjacentfirst physical sides by a predetermined distance; a second paving stonehaving the virtual perimeter outline and a plurality of second physicalsides, where each segment of the plurality of segments corresponds totwo or more of the second physical sides, and wherein any vertex betweentwo adjacent segments is separated from any vertex between two adjacentsecond physical sides by a predetermined distance; and wherein theplurality of first physical sides is different from the plurality ofsecond physical sides.
 2. The paving system of claim 1 wherein thevirtual perimeter outline is a Cairo pentagon.
 3. The paving system ofclaim 1 wherein each end point of each segment is located at a pointbetween each end point of a closest physical side.
 4. The paving systemof claim 1 further comprising a third paving stone having the virtualperimeter outline and a plurality of third physical sides, where eachsegment of the plurality of segments corresponds to two or more of thethird physical sides and the plurality of third physical sides isdifferent from the plurality of first and second physical sides.
 5. Thepaving system of claim 1 further comprising a third paving stone havingthe virtual perimeter outline and a plurality of third physical sides,where each segment of the plurality of segments corresponds to two ormore of the third physical sides, and wherein any vertex between twoadjacent segments is separated from any vertex between two adjacentthird physical sides by a predetermined distance.
 6. The paving systemof claim 5 wherein the plurality of third physical sides is differentfrom the plurality of first physical sides and the plurality of secondphysical sides.
 7. The paving system of claim 1 further comprising athird paving stone having a first portion of the virtual perimeteroutline with a corresponding first portion of the segments and one ormore additional first segments and a plurality of third physical sides,where each segment of the plurality of segments of the first portion ofthe virtual perimeter outline corresponds to two or more of the thirdphysical sides, and wherein any vertex between two adjacent segments isseparated from any vertex between two adjacent third physical sides by apredetermined distance.
 8. The paving system of claim 7 wherein theplurality of third physical sides is different from the plurality offirst physical sides and the plurality of second physical sides.
 9. Thepaving system of claim 6 further comprising a fourth paving stone havinga second portion of the virtual perimeter outline with a correspondingsecond portion of the segments and one or more additional secondsegments and a plurality of fourth physical sides.
 10. The paving systemof claim 6 further comprising a fourth paving stone having a secondportion of the virtual perimeter outline with a corresponding secondportion of the segments and one or more additional second segments and aplurality of fourth physical sides, where each segment of the pluralityof segments of the second portion of the virtual perimeter outlinecorresponds to two or more of the fourth physical sides.
 11. The pavingsystem of claim 10 wherein the plurality of fourth physical sides isdifferent from the plurality of first physical sides, the plurality ofsecond physical sides and the plurality of third physical sides.
 12. Thepaving system of claim 6 further comprising a fourth paving stone havinga second portion of the virtual perimeter outline with a correspondingsecond portion of the segments and one or more additional secondsegments and a plurality of fourth physical sides, where each segment ofthe plurality of segments of the second portion of the virtual perimeteroutline corresponds to two or more of the fourth physical sides, andwherein any vertex between two adjacent segments is separated from anyvertex between two adjacent fourth physical sides by a predetermineddistance.
 13. The paving system of claim 1 further comprising a thirdpaving stone having the virtual perimeter outline and a plurality ofthird physical sides, wherein the plurality of third physical sides isdifferent from the plurality of first physical sides and the pluralityof second physical sides.
 14. The paving system of claim 13 furthercomprising a fourth paving stone having a first portion the virtualperimeter outline and a plurality of fourth physical sides.
 15. Thepaving system of claim 14 wherein the plurality of fourth physical sidesis different from the plurality of first physical sides, the pluralityof second physical sides and the plurality of third physical sides. 16.The paving system of claim 15 further comprising a fifth paving stonehaving a second portion the virtual perimeter outline and a plurality offifth physical sides.
 17. The paving system of claim 16 wherein theplurality of fifth physical sides is different from the plurality offirst physical sides, the plurality of second physical sides, theplurality of third physical sides and the plurality of fourth physicalsides.
 18. The paving system of claim 16 wherein the first portion ofthe virtual perimeter and the second portion of the virtual perimeterform the virtual perimeter when combined.
 19. The paving system of claim12 wherein each end point of each segment is located at a point betweeneach end point of a closest physical side.
 20. A paving systemcomprising: a first paving stone having a virtual perimeter outline anda plurality of first physical sides, the virtual perimeter outlinehaving a plurality of segments, where each segment of the plurality ofsegments corresponds to two or more of the first physical sides, andwherein any vertex between two adjacent segments is separated from anyvertex between two adjacent first physical sides by a predetermineddistance; a second paving stone having the virtual perimeter outline anda plurality of second physical sides, where each segment of theplurality of segments corresponds to two or more of the second physicalsides, and wherein any vertex between two adjacent segments is separatedfrom any vertex between two adjacent second physical sides by apredetermined distance; a third paving stone having the virtualperimeter outline and a plurality of third physical sides, where eachsegment of the plurality of segments corresponds to two or more of thethird physical sides, and wherein any vertex between two adjacentsegments is separated from any vertex between two adjacent thirdphysical sides by a predetermined distance, wherein the plurality ofthird physical sides is different from the plurality of first physicalsides and the plurality of second physical sides; a fourth paving stonehaving a second portion of the virtual perimeter outline with acorresponding second portion of the segments and one or more additionalsecond segments and a plurality of fourth physical sides, where eachsegment of the plurality of segments of the second portion of thevirtual perimeter outline corresponds to two or more of the fourthphysical sides, wherein the plurality of fourth physical sides isdifferent from the plurality of first physical sides, the plurality ofsecond physical sides and the plurality of third physical sides, andwherein any vertex between two adjacent segments is separated from anyvertex between two adjacent fourth physical sides by a predetermineddistance; a fifth paving stone having a second portion the virtualperimeter outline and a plurality of fifth physical sides, wherein theplurality of fifth physical sides is different from the plurality offirst physical sides, the plurality of second physical sides, theplurality of third physical sides and the plurality of fourth physicalsides, and wherein the first portion of the virtual perimeter and thesecond portion of the virtual perimeter form the virtual perimeter whencombined; wherein the plurality of first physical sides is differentfrom the plurality of second physical sides; wherein the virtualperimeter outline is a Cairo pentagon; and wherein each end point ofeach segment is located at a point between each end point of a closestphysical side.